C-bases en espacios producto.
C-Complete Systems In Normed Spaces
Characterising subspaces of Banach spaces with a Schauder basis having the shift property
We give an intrinsic characterisation of the separable reflexive Banach spaces that embed into separable reflexive spaces with an unconditional basis all of whose normalised block sequences with the same growth rate are equivalent. This uses methods of E. Odell and T. Schlumprecht.
Characterization of Bessel sequences.
Let H be a separable Hilbert space, L(H) be the algebra of all bounded linear operators of H and Bess(H) be the set of all Bessel sequences of H. Fixed an orthonormal basis E = {ek}k∈N of H, a bijection αE: Bess(H) → L(H) can be defined. The aim of this paper is to characterize α-1E (A) for different classes of operators A ⊆ L(H). In particular, we characterize the Bessel sequences associated to injective operators, compact operators and Schatten p-classes.
Characterizations of completeness of normed spaces through weakly unconditionally Cauchy series
In this paper we obtain two new characterizations of completeness of a normed space through the behaviour of its weakly unconditionally Cauchy series. We also prove that barrelledness of a normed space can be characterized through the behaviour of its weakly- unconditionally Cauchy series in .
Characterizations of series in Banach spaces.
Characterizing translation invariant projections on Sobolev spaces on tori by the coset ring and Paley projections
We characterize those anisotropic Sobolev spaces on tori in the and uniform norms for which the idempotent multipliers have a description in terms of the coset ring of the dual group. These results are deduced from more general theorems concerning invariant projections on vector-valued function spaces on tori. This paper is a continuation of the author’s earlier paper [W].
Chebyshevian splines [Book]
Classification, through coordinates, of M-bases in separable Banach spaces.
Colacunary sequences in L-spaces
Comments to Enflo's construction of Banach space without the approximation property
Compact diagonal linear operators on Banach spaces with unconditional bases.
Conditionality constants of quasi-greedy bases in super-reflexive Banach spaces
We show that in a super-reflexive Banach space, the conditionality constants of a quasi-greedy basis ℬ grow at most like for some 0 < ε < 1. This extends results by the third-named author and Wojtaszczyk (2014), where this property was shown for quasi-greedy bases in for 1 < p < ∞. We also give an example of a quasi-greedy basis ℬ in a reflexive Banach space with .
Constructing non-compact operators into c₀
We prove that for each dense non-compact linear operator S: X → Y between Banach spaces there is a linear operator T: Y → c₀ such that the operator TS: X → c₀ is not compact. This generalizes the Josefson-Nissenzweig Theorem.
Construction of an orthonormal basis in and
Continuous mappings of a Banach space into a space
Contre-exemple à la propriété d'approximation uniforme dans les espaces de Banach
Convergence of greedy approximation I. General systems
We consider convergence of thresholding type approximations with regard to general complete minimal systems eₙ in a quasi-Banach space X. Thresholding approximations are defined as follows. Let eₙ* ⊂ X* be the conjugate (dual) system to eₙ; then define for ε > 0 and x ∈ X the thresholding approximations as , where . We study a generalized version of that we call the weak thresholding approximation. We modify the in the following way. For ε > 0, t ∈ (0,1) we set and consider the weak...
Convergence of series and isomorphic embeddings in Banach spaces
Corrigendum to "The Moment Problem in the Space C...(S)''.